Holography without strings?

TL;DR

This paper argues that holographic duality can emerge from bulk gravitational Gauss law and quantum entanglement without requiring stringy degrees of freedom, demonstrated through a toy scalar field model.

Contribution

It shows that holography arises from boundary conditions and entanglement, not necessarily from string theory, using a simplified scalar field model as proof of concept.

Findings

Holography can be derived from Gauss law and entanglement alone.

Boundary observables determine bulk observables in the model.

The model's Hamiltonian is essentially self-adjoint, supporting holography without strings.

Abstract

A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density (\rho) sources what we call a pseudo-Newtonian potential (\Phi) through Poisson's equation on each constant time surface, but there is no back-reaction on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time t. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above.